First make sure your hardware is correctly installed and you have the latest drivers (or the most stable ones) for your mainboard/video/sound hardware. Also make sure you are running your desktop at 16bpp or 32bpp. DOSBox doesn't like 24bpp resolution.

Go to the folder where you installed DOSBox and edit (with Notepad for instance) a text file called dosbox.conf (yay! you guessed it... It's DOSBox configuration). Look for this section:

[sdl] # fullscreen -- Start dosbox directly in fullscreen. # fulldouble -- Use double buffering in fullscreen. # fullfixed -- Do […]
Show full quote

[sdl]
# fullscreen -- Start dosbox directly in fullscreen.
# fulldouble -- Use double buffering in fullscreen.
# fullfixed -- Don't resize the screen when in fullscreen.
# fullresolution -- What resolution to use for fullscreen, use together with fullfixed.
# output -- What to use for output: surface,overlay,opengl,openglnb,ddraw.
# hwscale -- Extra scaling of window if the output device supports hardware scaling.
# autolock -- Mouse will automatically lock, if you click on the screen.
# sensitiviy -- Mouse sensitivity.
# waitonerror -- Wait before closing the console if dosbox has an error.
# priority -- Priority levels for dosbox: lower,normal,higher,highest.
# Second entry behind the comma is for when dosbox is not focused/minimized.
# mapperfile -- File used to load/save the key/event mappings from.

fullscreen=false
fulldouble=false
fullfixed=false
fullresolution=640x480
output=surface

And make sure output=surface. Save changes and rerun DOSBox. Does it work now? If not, try setting a different setting (like overlay). If it's still not working try getting and replacing SDL.DLL from www.libsdl.org